During a softball game, a player running from second base to third base reaches a speed
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Answer:
See the answers below
Explanation:
In order to solve these problems, we must decompose the magnitudes of the velocities on the x & y-axes, using the angles that are given. It is important for a better understanding to look at the attached image and understand how the angles are located relative to the horizontal axis.
1.
The horizontal component of the angle can be found with the cosine function. While the vertical component can be found using the sine function of the angle.
Viy = 24*sin (40)
Viy = 15.42 [m/s]
2.
The horizontal component of the angle can be found with the cosine function.
Vix = 24*cos(40)
Vix = 18.38 [m/s]
3.
Vix = 55*cos(25)
Vix = 49.84 [m/s]
The density of 53.4 wt aqueous NaOH solution is 0.809 g/ml
Given data:
- The mass percent of NaOH is 53.4.
- Volume of NaOH diluted is 16.7 ml.
- The volume of diluted solution is 2.00 L =2000 ml.
- Concentration of diluted solution is 0.169 M.
First, we find the initial concentration of NaOH by using the following formulae,
M₁V₁ = M₂V₂
Where,
M₁ is the initial molarity of NaOH
M₂ is the molarity after dilution
V₁ is the initial volume of NaOH
V₂ is the final volume after dilution.
Substituting the values,
M₁ × 16.7 ml = 0.169 M × 2000 ml,
M₁ =
M₁ = 20.2 M.
Thus, the initial concentration of NaOH is 20.2 M.
we know, 1 M solution contains 1 mol of substance present in 1 L solution,
Thus, 20.2 M solution will have 20.2 mols of NaOH.
Now, we can find the mass of NaOH by using the number of moles and molar mass.
- molar mass of NaOH is 40 g/mol.
Mass = no. of moles × molar mass
= 20.2 mol × 40 g/mol
= 808 g.
Thus, the mass of NaOH is 808g.
53.4 wt of NaOH means 53.4 g of NaOH in a 100 g solution,
Thus, 808 g of NaOH will be present in ,
⇒
⇒ 1513.1 g
Now, Convert the grams of NaOH to milliliters, using the density of NaOH at room temperature.
- The density of NaOH at room temperature is 1.515 g/ml,
Density =
⇒ 1.515 g/mol =
⇒ volume =
⇒ volume = 998.7 ml.
Thus, the volume of NaOH is 998.7 ml.
Hence, we know,
- the mass of NaOH is 808 g
- the volume of NaOH is 998.7 ml
Substituting the values,
Density = 808 g / 998.7 g/ml
⇒ Density = 0.809 g/ml
Thus, the density of 53.4 wt aqueous NaOH is 0.809 g/ml.
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